Using Cramer-rao Bound to Evaluate the Far- Field Sound Field Control Effect of the Low- Frequency Phased Array Emitting the Differ- Ent Weight Vectors

The theory and simulation studies were developed to analyze the far-field sound field control effect of the low-frequency phased array emitting the different weight vectors. Firstly, combining the adiabatic normal mode theory, the sonar-target model excited by the phased array was derived. Based on the model, the relationship between the weight vector and the Cramer-Rao lower bounds (CRB) of time-delay and Doppler frequency-shift estimations were set up theoretically. Secondly, using the CRBs to evaluate the far-field sound control effect of the phased array emitting the several weight vectors were computed according to the simulated environment. Finally, under the same energy input conditions, from the simulating results, it was showed that the phased array emitting the No.1 normal mode was not always the optimum in the far-field sound field control.